1. Field of the Invention
The preferred embodiments are directed to a controller for a scanning probe microscope (SPM), and more particularly, a controller for an SPM that enables improved scanning speeds while maintaining the ability to obtain high quality sample data.
2. Discussion of the Prior Art
A scanning probe microscope, such as an atomic force microscope (AFM) operates by providing relative scanning movement between a measuring probe and a sample while measuring one or more properties of the sample. A typical AFM system is shown schematically in FIG. 1. An AFM 10 employing a probe device 12 including a probe 14 having a cantilever 15. Scanner 24 generates relative motion between the probe 14 and sample 22 while the probe-sample interaction is measured. In this way images or other measurements of the sample can be obtained. Scanner 24 is typically comprised of one or more actuators that usually generate motion in three orthogonal directions (XYZ). Often, scanner 24 is a single integrated unit that includes one or more actuators to move either the sample or the probe in all three axes, for example, a piezoelectric tube actuator. Alternatively, the scanner may be an assembly of multiple separate actuators. Some AFMs separate the scanner into multiple components, for example an XY scanner that moves the sample and a separate Z-actuator that moves the probe.
In a common configuration, probe 14 is often coupled to an oscillating actuator or drive 16 that is used to drive probe 14 at or near a resonant frequency of cantilever 15. Alternative arrangements measure the deflection, torsion, or other motion of cantilever 15. Probe 14 is often a microfabricated cantilever with an integrated tip 17.
Commonly, an electronic signal is applied from an AC signal source 18 under control of an SPM controller 20 to cause actuator 16 (or alternatively scanner 24) to drive the probe 14 to oscillate. The probe-sample interaction is typically controlled via feedback by controller 20. Notably, the actuator 16 may be coupled to the scanner 24 and probe 14 but may be formed integrally with the cantilever 15 of probe 14 as part of a self-actuated cantilever/probe.
Often a selected probe 14 is oscillated and brought into contact with sample 22 as sample characteristics are monitored by detecting changes in one or more characteristics of the oscillation of probe 14, as described above. In this regard, a deflection detection apparatus 25 is typically employed to direct a beam towards the backside of probe 14, the beam then being reflected towards a detector 26, such as a four quadrant photodetector. Note that the sensing light source of apparatus 25 is typically a laser, often a visible or infrared laser diode. The sensing light beam can also be generated by other light sources, for example a He—Ne or other laser source, a superluminescent diode (SLD), an LED, an optical fiber, or any other light source that can be focused to a small spot. As the beam translates across detector 26, appropriate signals are transmitted to controller 20, which processes the signals to determine changes in the oscillation of probe 14. In general, controller 20 generates control signals to maintain a relative constant interaction between the tip and sample (or deflection of the lever 15), typically to maintain a setpoint characteristic of the oscillation of probe 14. For example, controller 20 is often used to maintain the oscillation amplitude at a setpoint value, AS, to insure a generally constant force between the tip and sample. Alternatively, a setpoint phase or frequency may be used.
A workstation is also provided, in the controller 20 and/or in a separate controller or system of connected or stand-alone controllers, that receives the collected data from the controller and manipulates the data obtained during scanning to perform point selection, curve fitting, and distance determining operations. The workstation can store the resulting information in memory, use it for additional calculations, and/or display it on a suitable monitor, and/or transmit it to another computer or device by wire or wirelessly. The memory may comprise any computer readable data storage medium, examples including but not limited to a computer RAM, hard disk, network storage, a flash drive, or a CD ROM. Notably, scanner 24 often comprises a piezoelectric stack (often referred to herein as a “piezo stack”) or piezoelectric tube that is used to generate relative motion between the measuring probe and the sample surface. A piezo stack is a device that moves in one or more directions based on voltages applied to electrodes disposed on the stack. Piezo stacks are often used in combination with mechanical flexures that serve to guide, constrain, and/or amplify the motion of the piezo stacks. Additionally, flexures are used to increase the stiffness of actuator in one or more axis, as described in copending application Ser. No. 11/687,304, filed Mar. 16, 2007, entitled “Fast-Scanning SPM Scanner and Method of Operating Same.” Actuators may be coupled to the probe, the sample, or both. Most typically, an actuator assembly is provided in the form of an XY-actuator that drives the probe or sample in a horizontal, or XY-plane and a Z-actuator that moves the probe or sample in a vertical or Z-direction.
As the utility of SPM continues to develop, a need has arisen for imaging different types of samples at greater speeds to improve sample measurement throughput (e.g., more than 20 samples per hour) and/or measure nanoscale processes with higher time resolution than currently available. Although AFM imaging provides high spatial resolution (nanoscale), it has generally low temporal resolution. Typical high quality AFM images take several minutes to acquire, especially for scan sizes above a few microns.
Several factors can limit imaging speed, including the cantilever response time, the usable scanner bandwidth in X, Y and Z directions, the power and bandwidth of the high voltage amplifier that drives the scanner, the speed of the cantilever force sensing, as well as the demodulation system and the tracking force feedback system.
SPM images are typically constructed of arrays of measurements recorded at different locations on the sample. For example, an image may contain the local value of the relative sample height measured over an array of different XY locations on the sample. Alternative measurements can include amplitude, phase, frequency of the cantilever, electric and magnetic forces, friction, stiffness of the sample, etc.
In this regard, relative positioning between the probe and sample is very important. The quality of the acquired data, and resultant image(s), depends on the system knowing the precise location where data is collected. It follows that position errors cause image degradation, a problem exacerbated by operating the AFM at greater bandwidths.
A significant challenge in this regard is that piezoelectric stacks, tubes and other types of SPM actuators are imperfect. When considering desired scanning motion, the ideal behavior would be actuator movement substantially linearly in proportion to the voltage or other control signal applied. Instead, actuators, including piezo stacks, often move in a non-uniform manner, meaning that their sensitivity (e.g., nanometers of motion vs. applied voltage) can vary as the voltage increases. Moreover, drift, hysteresis and creep of the actuator operate to further compromise precisely positioning the probe and/or sample. With respect to hysteresis, for example, the response to an incremental voltage change will depend on the history of previous voltages applied to the actuator. Hysteresis can therefore cause a large prior motion to compromise the response to a commanded move, even many minutes later. After the command voltage is applied, the piezo may move a desired distance, but continues to move uncontrollably due to the creep effect. Such effect can be more than 10% of the commanded motion, causing a substantial positioning error.
Notably, these issues exist whether the probe device of the AFM is coupled to the actuator (i.e., the case in which the probe device moves in three orthogonal directions), or the sample is coupled to the actuator. Moreover, though known solutions attempt to overcome the above-noted challenges, they have been imperfect.
For example, some open loop methods of driving the SPM actuator have been implemented in an attempt to compensate for limitations of the controller and actuators, and thereby limit poor tracking between desired scanning movement and actual movement. The actuators may be calibrated, for example, by applying a voltage, for example, to the X-Y actuators and then measuring the actual distance that the sample or probe travels. A look-up table may then be created, and then, in operation, the actuator position can be estimated by monitoring the voltage that is applied to the X-Y and/or Z actuators. In another open loop alternative, the scanner and its motion can be modeled using rigorous mathematical techniques.
More specifically in this regard, turning to FIG. 2, open loop solutions typically involve providing a unique drive signal uo 41 that is applied to an actuator or scanner 42 of an AFM 40 to provide scanning motion between the AFM probe and the sample. The drive signal is derived, for example, from a model or a look-up table and corresponds to the desired motion of the actuator. The drive signal uo is intended to produce actual scanner motion that substantially tracks the desired motion to produce uniform scanning. See for example U.S. Pat. No. 5,557,156, owned by Veeco Instruments; Inc., which describes applying non-linear drive voltages having a shape defined by a set of pre-calibrated data, to piezo actuators to drive them into substantially linear motion. The set of data may also be called a scan table. This technique has been successful for counteracting actuator non-linearities, but the calibration procedure is cumbersome and it does not adequately address drift and creep. Additionally, the actuator response depends strongly on scan speed requiring increasingly complex calibration and lookup tables as SPM scan speed increases. When the scanner turns around for scanning the next line or offsets to a different position, a transient response can be excited. Such transients can compromise data integrity. For example, transients 43 shown in FIG. 2 can exist at the turn points of a typical raster scan drive 41. Notably, to minimize transients at turning points, an alternative drive may be employed. As shown in FIG. 3, an AFM 44 may employ a drive 45 that is rounded at the turn points. This solution operates well to quiet transients at a relatively low scan rate, but at the higher scan rate the scanner motion (as shown by curve 46) still does not follow the desired trajectory (raster scan corresponding to the triangle wave form 47) in most cases. Moreover, due to the rounding, the usable range of the drive is limited.
Because such open loop solutions can be complicated and often still do not provide acceptable position accuracy, especially at higher scan speeds, some SPMs employ closed loop position control. Such systems improve accuracy by using an auxiliary position sensor in a feedback arrangement to actively monitor actuator movement, i.e., to determine how well the actual movement is tracking the commanded movement, and dynamically adjusting the control signal applied to the appropriate SPM actuator(s). In this way, the actuator can be driven in a linear way to follow a predetermined trajectory, compensating for non-linearity, hysteresis, and drift simultaneously. As a result, more accurate images can be obtained. However, the bandwidth of the position control feedback is often limited (discussed below), and the noise introduced by the sensor employed to detect actual scanner motion can degrade image quality through the feedback loop, thus further limiting the ability of the AFM to track a fast command signal during scanning, and thus produce acceptable images, at greater speeds. Due to the noise limitation, many position control feedback systems are disabled at small scan sizes. In sum, at higher imaging speeds, the performance of the position feedback system often degrades SPM system performance.
Returning to the details of closed loop position control, we turn to FIG. 4. A closed loop control system 50 is used to drive the actuator to follow a desired trajectory while minimizing position errors. A reference waveform 51 is generated as model for the desired scanner motion, a triangle wave in the example. Position sensor 54 measures the actual movement of scanner 52 and transmits that sensed signal to a summing block 56 (e.g., a digital sum or analog summing circuitry) that generates an error signal representing the difference between the desired motion of the scanner and actual scanner movement. Several auxiliary displacement or position sensors have been proposed and/or used for monitoring actuator movement, including Linear Variable Displacement Transducers (LVDTs), capacitance sensors, strain gauge and inductance sensors, and optical sensors including, for example, optical displacement sensors (ODSs) and optical interferometers. Any alternative sensor that provides a predictable and calibratable output as a function of relative position may be used. These sensors typically operate as part of a closed loop controller associated with the scanner to correct for differences between desired and actual movement.
A controller 58, such as a proportion and integral (PI) controller (or, for example, a double integrator) generates a control signal, uc, in response to the error signal which is used to drive the scanner. Controllers have been implemented with both all analog electronics and digital feedback loops run by digital signal processors (DSP), field programmable gate arrays (FPGA) and other embedded controller and digital computing devices, including personal computers. The control signal operates to compensate for measured position error produced by the scanner, for example, caused by creep and drift.
Although useful for minimizing the effects of system conditions that have an adverse impact on the ability of the scanner to track desired motion, the bandwidth of conventional control systems 50 is limited. There are several reasons for the limits in conventional position control systems, including scanner resonances and position sensor noise and bandwidth limitations.
First, the resonant properties of the scanner must be considered. Each turnaround in the triangle wave reference waveform 51 creates a substantial impulse force on the scanner that can excite unwanted parasitic resonances. These resonances can also couple between axes and show up in the measured motion of the cantilever's relative motion vis-à-vis the sample. Conventional AFMs either scan slow enough to reduce the amplitude of unwanted oscillation to an acceptable level and/or trade off some scan range to round the tops and bottoms of the triangle wave reference, as noted previously in connection with the open loop system shown in FIG. 3. The inability of SPM scanners to scan large areas at high speeds without unwanted oscillations is a major bottleneck to operating SPMs at greater speeds.
Additionally, these resonances limit how fast the controller 58 can operate. A feedback loop will go unstable if there is a gain of more than one with a phase shift of 180 degrees. A simple mechanical resonance of the scanner will accumulate 90 degrees of phase shift and a substantial gain amplification at the resonance peak. The gain (and hence bandwidth) of controller 58 is limited to compensate for the phase shift and gain of the scanner's mechanical resonance(s). Even before the condition of instability, underdamped resonances can cause oscillations and overshoot in the actual motion of the scanner. As a result, operation of conventional position control feedback loops is limited to a small fraction of the scanner's lowest observed resonance, or “fundamental resonant frequency.” Notably, the lowest observed resonance is most often axis dependent, with coupling of the response typically being present among axes, thereby limiting the lowest observed resonance of the scanner/actuator.
Moreover, sensor 54 introduces noise to the system that compromises the controller's ability to satisfactorily track the desired motion. The impact of sensor noise is shown schematically in FIG. 4. (In practice, of course, the sensor noise accompanies the signal) Both the scanner's real position and the sensor noise (signal 55) are compared to the reference and the resultant error processed by controller 58. The controller thus attempts to have the scanner respond to both the real position error and the unwanted sensor noise, thus producing actuator motion illustrated by signal 53. The resulting image is therefore correspondingly compromised by all the sensor noise that is within the feedback bandwidth. The control signal uc, though compensating for system dynamics including thermal drift and creep, may not yield the desired scanner motion because of the additional high frequency noise introduced via the sensing scheme. Sensor noise is typically a function of bandwidth, so the position sensor electronics and/or the controller may limit the bandwidth of the sampled position sensor signal to reduce the image of this noise. The effect of a limited sensor bandwidth, however, is typically the accumulation of phase shifts in the sensor output versus the actual motion of the scanner. These phase shifts then limit the maximum gain and bandwidth that can be employed by the controller 58. The practical effect of sensor noise and bandwidth in this case is that the speed of scanning must be correspondingly reduced to maintain an acceptable level of position noise for acquiring high quality data.
Several groups have also developed schemes to counteract the effects of unwanted resonances of the scanner by developing model based control schemes. Authors on this subject include Stemmer, Schitter, Ando, Salapaka, and Zou, for example. In a typical model-based controller for SPM, the dynamic properties of the scanner are measured and an optimal closed-loop control scheme is designed to maintain stability of the feedback loop over a wide bandwidth. A typical first step is system identification, a procedure that maps the amplitude and phase response of the scanner versus frequency, defining characteristics known as the “transfer function.” This transfer function may be used in a controller that achieves the highest scanner bandwidth, while also attempting to minimize oscillations due to unwanted resonances. Typical closed loop control strategies in this regard include H-infinity or H2 controllers that are described in the literature. Alternative schemes include intentionally adding impulse transients to the control waveform timed to counteract the impulse at the triangle wave turn-around. For example, an impulse force can be applied to the scanner at a time corresponding to half the oscillation period of the fundamental resonance. Destructive interference will occur between the results of the two impulses and quickly damp the unwanted oscillation. That said, because such closed loop schemes are intended to operate over a wide bandwidth, the problems associated with sensor noise continue to limit system performance.
An open loop model based controller, while compensating for scanner resonances, will still be subject to unwanted motion within the system, including scanner nonlinearities, creep and thermal drift. Thus, tracking in such systems remains imperfect. To accommodate degraded image quality, open loop feed forward controllers have been developed that attempt to model system factors, such as nonlinearities, creep and thermal drift, that impact the resultant data to produce an optimized drive waveform. Such models associated with feed forward controllers are difficult to control and typically produce less than ideal results, primarily due to the challenge of creating a workable model that fits all desired imaging conditions. Such imaging conditions often produce a change in the mechanical environment and therefore a change of the transfer function used in the model. Ultimately, producing linear scanner motion is very difficult to achieve with these open loop solutions. Therefore, an improvement was desired.
In the end, most often the design of the AFM must navigate a tradeoff between low noise performance (e.g., open loop) and image positioning accuracy (e.g., closed loop). According to one type of open loop AFM scan controller, the control scheme utilizes a calibrated scanner and corresponding input signal, such as a modified triangle wave, that is configured to account for system irregularities (e.g., resonances) when scanning. Such open loop systems utilizing a feed forward model minimize adverse effects on positioning due to system noise because extraneous structure (such as an auxiliary sensor) is minimized. However, accurate operation of the scanner and ultimate image accuracy is controlled by the system's ability to accurately characterize the scanner and otherwise account for environmental effects such as drift and creep. This is most often a difficult task that typically yields an imperfect result, given the inability to accurately model or predict particular environmental conditions. Moreover, due to this difficulty, such systems are not sufficiently robust for many applications. The open loop feed forward scheme can be effective in compensating the scanner non-linearity if the calibration is accurate and remains constant throughout the usage, but it still does not address the resonance distortion introduced by the impulse forces at the turning point of the linear triangular scanning.
The field of scanning probe microscopy was thus in need of a controller that facilitates tracking fast scanner movement with low noise while also compensating for position skewing operational conditions such as thermal drift and creep. Ideally, a closed loop scanner that minimizes the impact of sensor noise on system performance was desired.